Yeah, when my now wife and I lived in Idaho for a summer, finding a place to rent to both of us was very difficult, especially from a distance. Seems that pretty much all landlords didn't allow mixed gender tenants who weren't married. We eventually found one who broke their own rule with a wink and a nod. They knew we were engaged, but submitted the paperwork as if we were siblings or something. Not sure if it was a law we were skirting, or just a more reasonable "local" landlord lying to a boss. Either way, we broke some sort of rule with not only the knowledge of the landlord, but the landlord was an actual accomplice. It was about our 20th choice, the first 19 were not willing to allow it to happen.
Advice. Sell the bigger stuff that's tough to haul, buy new stuff out there. Pack both cars full. Tow the 2nd car, and drive together to take turns with driving duties. Treat the drive itself as an adventure. Give yourself plenty of time, with plans to spend a little time in "touristy" places such as the Badlands, Mount Rushmore, Yellowstone, etc.
Once you're past greater Chicago, the actual driving is VERY easy.